I read some articles mostly claiming that if neutrino is their own antimatter than they could get their mass from some other source rather than the higgs field, and I can't probe any further because they said it is still a mystery. What wrong with neutrino when Z boson which is their own antimatter can get their mass from interacting with higgs field?
In the Standard Model, neutrinos only interact with anything else via the weak force, and the weak force only interacts with particles with left-handed chirality*. Therefore, every neutrino in the Standard Model is left-handed**.
The Higgs boson gives the electroweak bosons mass in a fundamental process called electroweak symmetry breaking. It is also thought that the Higgs gives fermions (i.e. the quarks and non-neutrino leptons) their mass through a different mechanism, namely the Yukawa coupling. The Yukawa coupling is formulated in such a way that the fermion in question changes chirality whenever it interacts with the Higgs boson***, so right-handed fermions change into left-handed fermions and vice versa.
This is where the problem comes from: neutrinos, as far as we know, can only be left-handed. If they can't be right-handed, then it's impossible to interact with the Higgs field via the Yukawa coupling. This is why neutrinos are not currently thought to get their mass from the Higgs field.
*This strange property is often given the name "parity violation."
**Right-handed "sterile" neutrinos, which don't interact with anything else and can only be seen if we notice the absence of something else, have been theorized to exist. Search experiments are currently running to find sterile neutrinos (e.g. by recording missing energy in a collider, or by noticing that neutrino mixing tends to make neutrinos seem to disappear), but none have recorded any evidence of their existence.
***This is necessarily oversimplified. See here for more details: https://www.quantumdiaries.org/2011/06/19/helicity-chirality-mass-and-the-higgs/